## The Trotter-Kato theorem and approximation of PDEs

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- by Kazufumi Ito and Franz Kappel PDF
- Math. Comp.
**67**(1998), 21-44 Request permission

## Abstract:

We present formulations of the Trotter-Kato theorem for approximation of linear C${}_0$-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.## References

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## Additional Information

**Kazufumi Ito**- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- Email: kito@eos.ncsu.edu
**Franz Kappel**- Affiliation: Institut für Mathematik, Universität Graz, Heinrichstraße 36, A8010 Graz, Austria
- Email: franz.kappel@kfunigraz.ac.at
- Received by editor(s): August 18, 1995
- Received by editor(s) in revised form: August 1, 1996
- Additional Notes: Research of the first author was supported in part by the NSF under Grant UINT-8521208 and DMS-8818530 and by the Air Force Office of Scientific Research under contract AFOSR-90-0091.

Research by the second author was supported in part by FWF(Austria) under Grants P6005, P8146-PHY and under F003. - © Copyright 1998 American Mathematical Society
- Journal: Math. Comp.
**67**(1998), 21-44 - MSC (1991): Primary 47D05, 47H05, 65J10, 35K22, 35L99
- DOI: https://doi.org/10.1090/S0025-5718-98-00915-6
- MathSciNet review: 1443120